Fluid Animation have dragged me through blood and sweat
Solution for Particle size:


Go in the domain cube and select the particle system that is generated in there (Liquid needs to be active in the domain for the particle system to show up!).
Find the Viewport Display Panel and change the Size to 0.001m instead of the 0.01m it was.

There seems to be something that sets the particle size back to 0.01m everytime. Did not happen in a new scene, but i do not know what settings or buttons where pressed in the run of creating the entire scene.


Solution for the cup:


Create a duplicate of the cup, you can call it "Simcup".
Remove all but the inner walls, also the subdivision surface modifier can be set to 2 for both, render and view. It's also a good idea to make the Simcup a child of the original cup, so it sticks to it.
Add a solidify modifier and set the thickness to 0.015m

To have the simcup not disturb the render and or viewport, go in the Object Properties and there to the Visibility and deactivate the "Show in Render", then in the Viewport Display deactivate "Shadow" and set Display As to "Bounds"

Now remove the Fluid simulation from the cup. The simcup on the other hand keeps it, as it was copied when you duplicated it.
The Sampling Substeps seem to be a good value with 5 and the Surface Thickness worked well with 0.01



Suggestion for the inflow:
The cylinder was to big and caused the cup to always be flooded and overfilled.
Adjusting it down a bit and reducing the time the inflow is open helps a lot.

And finally the domain, aside the fact that it can be scaled down (in edit mode please), you can change settings and try on Replay mode, for that it's best to set the time on 1 and then deactivate and reactivate the Fluid modifier visibility, seems to be a lot better then deleting the cache every time. Learned something new here too :)

One setting to consider is the Diffusion, where you can use the preset water.

After clicking on the "Water" entry you have to move your mouse out of the popup.
Also, make sure to set the Real World Size value to the right size.(I scaled the cube down and used the longest side Z)

If you want to start the liquid inflow at a certain time, you can save yourself a lot cache by starting the simulation at that time, though the keys for the inflow you had already set, i started at 1 for convenience while testing.

So try and test around until you are happy and once it's looking fine, you can increase the resolution for more details if needed, then switch the "Domain Cache" Type to Final and press Bake All.

Updated with little explanation:
The Domain in regards to liquid simulations takes the place of the liquid itself, but only for the time it is simulated as mesh. So if the simulation is running from frame 1 to 100 you must expect the domain cube to show up again from frame 101 onward. That problem can usually be solved by giving the simulation a bit more time to settle and then exchanging a still of the simulations last frame with the domain. The Object used for the inflow can be set invisible after the simulation is baked in mesh as the liquid will take it's place, except in case that the inflow is hidden anyway, like in a pipe or such.

Here two visual motivations:



Happy Blending